Pandas Profiling Report

Dataset statistics

Number of variables	9
Number of observations	500
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	35.3 KiB
Average record size in memory	72.3 B

Variable types

NUM	8
BOOL	1

Warnings

Serial No. has unique values Unique

Reproduction

Analysis started	2020-09-28 14:22:11.512681
Analysis finished	2020-09-28 14:22:25.165745
Duration	13.65 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

Serial No.
Real number (ℝ_≥0)

UNIQUE

Distinct	500
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	250.5
Minimum	1
Maximum	500
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	25.95
Q1	125.75
median	250.5
Q3	375.25
95-th percentile	475.05
Maximum	500
Range	499
Interquartile range (IQR)	249.5

Descriptive statistics

Standard deviation	144.4818328
Coefficient of variation (CV)	0.5767737835
Kurtosis	-1.2
Mean	250.5
Median Absolute Deviation (MAD)	125
Skewness	0
Sum	125250
Variance	20875
Monotocity	Strictly increasing

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
500	1	0.2%
171	1	0.2%
158	1	0.2%
159	1	0.2%
160	1	0.2%
161	1	0.2%
162	1	0.2%
163	1	0.2%
164	1	0.2%
165	1	0.2%
Other values (490)	490	98.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.2%
2	1	0.2%
3	1	0.2%
4	1	0.2%
5	1	0.2%

Value	Count	Frequency (%)
500	1	0.2%
499	1	0.2%
498	1	0.2%
497	1	0.2%
496	1	0.2%

GRE Score
Real number (ℝ_≥0)

Distinct	49
Distinct (%)	9.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	316.472
Minimum	290
Maximum	340
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	290
5-th percentile	298
Q1	308
median	317
Q3	325
95-th percentile	335
Maximum	340
Range	50
Interquartile range (IQR)	17

Descriptive statistics

Standard deviation	11.29514837
Coefficient of variation (CV)	0.03569083007
Kurtosis	-0.7110644626
Mean	316.472
Median Absolute Deviation (MAD)	8
Skewness	-0.03984185809
Sum	158236
Variance	127.5803768
Monotocity	Not monotonic

Histogram with fixed size bins (bins=49)

Value	Count	Frequency (%)
312	24	4.8%
324	23	4.6%
316	18	3.6%
321	17	3.4%
322	17	3.4%
327	17	3.4%
314	16	3.2%
311	16	3.2%
320	16	3.2%
317	15	3.0%
Other values (39)	321	64.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
290	2	0.4%
293	1	0.2%
294	2	0.4%
295	5	1.0%
296	5	1.0%

Value	Count	Frequency (%)
340	9	1.8%
339	3	0.6%
338	4	0.8%
337	2	0.4%
336	5	1.0%

TOEFL Score
Real number (ℝ_≥0)

Distinct	29
Distinct (%)	5.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	107.192
Minimum	92
Maximum	120
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	92
5-th percentile	98
Q1	103
median	107
Q3	112
95-th percentile	118
Maximum	120
Range	28
Interquartile range (IQR)	9

Descriptive statistics

Standard deviation	6.08186766
Coefficient of variation (CV)	0.05673807429
Kurtosis	-0.6532454042
Mean	107.192
Median Absolute Deviation (MAD)	5
Skewness	0.09560097236
Sum	53596
Variance	36.98911423
Monotocity	Not monotonic

Histogram with fixed size bins (bins=29)

Value	Count	Frequency (%)
110	44	8.8%
105	37	7.4%
104	29	5.8%
112	28	5.6%
107	28	5.6%
106	28	5.6%
103	25	5.0%
102	24	4.8%
100	24	4.8%
99	23	4.6%
Other values (19)	210	42.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
92	1	0.2%
93	2	0.4%
94	2	0.4%
95	3	0.6%
96	6	1.2%

Value	Count	Frequency (%)
120	9	1.8%
119	10	2.0%
118	10	2.0%
117	8	1.6%
116	16	3.2%

University Rating
Real number (ℝ_≥0)

Distinct	5
Distinct (%)	1.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.114
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	2
median	3
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	2

Descriptive statistics

Standard deviation	1.143511801
Coefficient of variation (CV)	0.3672163779
Kurtosis	-0.8100796635
Mean	3.114
Median Absolute Deviation (MAD)	1
Skewness	0.09029498313
Sum	1557
Variance	1.307619238
Monotocity	Not monotonic

Histogram with fixed size bins (bins=5)

Value	Count	Frequency (%)
3	162	32.4%
2	126	25.2%
4	105	21.0%
5	73	14.6%
1	34	6.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	34	6.8%
2	126	25.2%
3	162	32.4%
4	105	21.0%
5	73	14.6%

Value	Count	Frequency (%)
5	73	14.6%
4	105	21.0%
3	162	32.4%
2	126	25.2%
1	34	6.8%

SOP
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	1.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.374
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	1.5
Q1	2.5
median	3.5
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	1.5

Descriptive statistics

Standard deviation	0.9910036208
Coefficient of variation (CV)	0.2937177299
Kurtosis	-0.7057169536
Mean	3.374
Median Absolute Deviation (MAD)	0.5
Skewness	-0.2289723963
Sum	1687
Variance	0.9820881764
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
4	89	17.8%
3.5	88	17.6%
3	80	16.0%
2.5	64	12.8%
4.5	63	12.6%
2	43	8.6%
5	42	8.4%
1.5	25	5.0%
1	6	1.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	6	1.2%
1.5	25	5.0%
2	43	8.6%
2.5	64	12.8%
3	80	16.0%

Value	Count	Frequency (%)
5	42	8.4%
4.5	63	12.6%
4	89	17.8%
3.5	88	17.6%
3	80	16.0%

LOR
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	1.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.484
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	2
Q1	3
median	3.5
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	0.9254495739
Coefficient of variation (CV)	0.2656284655
Kurtosis	-0.7457485106
Mean	3.484
Median Absolute Deviation (MAD)	0.5
Skewness	-0.1452903146
Sum	1742
Variance	0.8564569138
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
3	99	19.8%
4	94	18.8%
3.5	86	17.2%
4.5	63	12.6%
5	50	10.0%
2.5	50	10.0%
2	46	9.2%
1.5	11	2.2%
1	1	0.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.2%
1.5	11	2.2%
2	46	9.2%
2.5	50	10.0%
3	99	19.8%

Value	Count	Frequency (%)
5	50	10.0%
4.5	63	12.6%
4	94	18.8%
3.5	86	17.2%
3	99	19.8%

CGPA
Real number (ℝ_≥0)

Distinct	184
Distinct (%)	36.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	8.57644
Minimum	6.8
Maximum	9.92
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	6.8
5-th percentile	7.638
Q1	8.1275
median	8.56
Q3	9.04
95-th percentile	9.6
Maximum	9.92
Range	3.12
Interquartile range (IQR)	0.9125

Descriptive statistics

Standard deviation	0.6048128003
Coefficient of variation (CV)	0.07052026253
Kurtosis	-0.5612783981
Mean	8.57644
Median Absolute Deviation (MAD)	0.46
Skewness	-0.02661251732
Sum	4288.22
Variance	0.3657985234
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
8	9	1.8%
8.76	9	1.8%
8.54	7	1.4%
8.45	7	1.4%
8.56	7	1.4%
8.12	7	1.4%
7.88	6	1.2%
8.64	6	1.2%
8.66	6	1.2%
9.11	6	1.2%
Other values (174)	430	86.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
6.8	1	0.2%
7.2	1	0.2%
7.21	1	0.2%
7.23	1	0.2%
7.25	1	0.2%

Value	Count	Frequency (%)
9.92	1	0.2%
9.91	1	0.2%
9.87	2	0.4%
9.86	1	0.2%
9.82	1	0.2%

Research
Boolean

Distinct	2
Distinct (%)	0.4%
Missing	0
Missing (%)	0.0%
Memory size	3.9 KiB

1	280
0	220

Common Values
Chart

Value	Count	Frequency (%)
1	280	56.0%
0	220	44.0%

Chance of Admit
Real number (ℝ_≥0)

Distinct	61
Distinct (%)	12.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.72174
Minimum	0.34
Maximum	0.97
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	0.34
5-th percentile	0.47
Q1	0.63
median	0.72
Q3	0.82
95-th percentile	0.94
Maximum	0.97
Range	0.63
Interquartile range (IQR)	0.19

Descriptive statistics

Standard deviation	0.141140404
Coefficient of variation (CV)	0.1955557458
Kurtosis	-0.4546817998
Mean	0.72174
Median Absolute Deviation (MAD)	0.1
Skewness	-0.28996621
Sum	360.87
Variance	0.01992061363
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.71	23	4.6%
0.64	19	3.8%
0.73	18	3.6%
0.72	16	3.2%
0.79	16	3.2%
0.78	15	3.0%
0.76	14	2.8%
0.8	13	2.6%
0.7	13	2.6%
0.94	13	2.6%
Other values (51)	340	68.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.34	2	0.4%
0.36	2	0.4%
0.37	1	0.2%
0.38	2	0.4%
0.39	1	0.2%

Value	Count	Frequency (%)
0.97	4	0.8%
0.96	8	1.6%
0.95	5	1.0%
0.94	13	2.6%
0.93	12	2.4%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

First rows

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
0	1	337	118	4	4.5	4.5	9.65	1	0.92
1	2	324	107	4	4.0	4.5	8.87	1	0.76
2	3	316	104	3	3.0	3.5	8.00	1	0.72
3	4	322	110	3	3.5	2.5	8.67	1	0.80
4	5	314	103	2	2.0	3.0	8.21	0	0.65
5	6	330	115	5	4.5	3.0	9.34	1	0.90
6	7	321	109	3	3.0	4.0	8.20	1	0.75
7	8	308	101	2	3.0	4.0	7.90	0	0.68
8	9	302	102	1	2.0	1.5	8.00	0	0.50
9	10	323	108	3	3.5	3.0	8.60	0	0.45

Last rows

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
490	491	307	105	2	2.5	4.5	8.12	1	0.67
491	492	297	99	4	3.0	3.5	7.81	0	0.54
492	493	298	101	4	2.5	4.5	7.69	1	0.53
493	494	300	95	2	3.0	1.5	8.22	1	0.62
494	495	301	99	3	2.5	2.0	8.45	1	0.68
495	496	332	108	5	4.5	4.0	9.02	1	0.87
496	497	337	117	5	5.0	5.0	9.87	1	0.96
497	498	330	120	5	4.5	5.0	9.56	1	0.93
498	499	312	103	4	4.0	5.0	8.43	0	0.73
499	500	327	113	4	4.5	4.5	9.04	0	0.84

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows